NEMS have demonstrated tremendous potential for applications such as ultrasensitive mass and force sensing. Nonetheless, because of their physical dimensions, their actuation and readout still remains as of today a challenge. It is known that their immediate surroundings can be the origin of the alteration of the extremely weak signals induced by their displacements.
In an M-NEMS system and in any oscillating system, frequency stability may be defined as the uncertainty of the measured frequency normalized to its mean value:
      ∂    f        f    0  where ∂f is the instantaneous frequency deviation and f0 the nominal frequency of the oscillator.
The extent to which M-NEMS sensors can resolve the mass of a particle is inherent to its resonant frequency stability and other properties including its mass. In such mass detection apparatus, the M-NEMS is part of a closed loop system forming an oscillator. When the resonance fluctuates, so does the oscillation frequency and it translates into frequency instability of the oscillator.
This stability is thought to reach a limit with the resonator's ability to resolve thermally-induced vibrations. Although measurements and predictions of resonator stability usually disregard fluctuations in the mechanical frequency response, these fluctuations have recently attracted considerable interest. However, their existence is very difficult to demonstrate experimentally.
To date, all measurements of their frequency stability report values several orders of magnitude larger than the limit imposed by thermomechanical noise. In such system, frequency instability of the oscillator may be caused by two phenomena, additive noise and intrinsic frequency fluctuations of the resonator. But there is no diagnostic tool or means to distinguish one phenomenon from another.
There are tools and means to characterize the frequency stability of an oscillating system. The document “Standard terminology for fundamental frequency and time metrology” authored by D. Allan et al. puts an emphasis on some of these tools. They are known as the Allan Deviation, the Power Spectral Density and the Phase Spectral Density. They are strongly related, complementary and globally show the same information but in a different manner and domain. Thus, processes such as random walk frequency, flicker frequency, white frequency, flicker phase and white phase noises may be identified with these tools. These diagnostic tools are extensively used by the frequency metrology community but are not always sufficient, such as in the case of the problem solved by the present invention.
The power spectral density is probably the most straightforward analysis. It is a direct measurement performed with a spectrum analyzer at the output of the device under test without any external measurement system. That said it is also the least effective in terms of identifying different types of noises processes.
The phase spectral density measurement is more complex to implement. One of the simplest ways by which it is obtained is with a residual phase noise measurement system. Two near identical devices under test are beat together while they are forming a phase bridge. A phase shifter placed in one of the arms of the bridge sets a quadrature between the output signals of the two devices. The zero beat (DC signal) containing phase fluctuations is then measured with a vector signal analyzer then plotted in a normalized one hertz bandwidth as a function of carrier offset frequencies.
The Allan Deviation is a statistical tool also called the two-sample variance. It is a measure of the variability of the average frequency of an oscillator between two adjacent measurement intervals. For example the variation measurement of a frequency beat between two near identical oscillators with a frequency counter. The measurement occurs over a certain period of time, during which the frequency counter probes repeatedly the intermediate frequency port of the mixer for an integration time of duration Tau.